Information on Result #1466419
Linear OOA(3243, 4194386, F3, 2, 22) (dual of [(4194386, 2), 8388529, 23]-NRT-code), using (u, u+v)-construction based on
- linear OOA(332, 85, F3, 2, 11) (dual of [(85, 2), 138, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(332, 85, F3, 11) (dual of [85, 53, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(332, 87, F3, 11) (dual of [87, 55, 12]-code), using
- (u, u+v)-construction [i] based on
- linear OA(35, 6, F3, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,3)), using
- dual of repetition code with length 6 [i]
- linear OA(327, 81, F3, 11) (dual of [81, 54, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(35, 6, F3, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,3)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(332, 87, F3, 11) (dual of [87, 55, 12]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(332, 85, F3, 11) (dual of [85, 53, 12]-code), using
- linear OOA(3211, 4194301, F3, 2, 22) (dual of [(4194301, 2), 8388391, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3211, large, F3, 22) (dual of [large, large−211, 23]-code), using
- OOA 2-folding [i] based on linear OA(3211, 8388602, F3, 22) (dual of [8388602, 8388391, 23]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3243, 4194386, F3, 3, 22) (dual of [(4194386, 3), 12582915, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3243, 4194386, F3, 4, 22) (dual of [(4194386, 4), 16777301, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(3243, 4194386, F3, 5, 22) (dual of [(4194386, 5), 20971687, 23]-NRT-code) | [i] | ||
| 4 | Digital (221, 243, 4194386)-net over F3 | [i] | ||